Efficiency, Sankey diagrams, and work done

For ages 12–13 (GCSE lead-in / NGSS HS placement), this procedural topic covers three linked quantitative skills: efficiency = useful output ÷ total input (as a ratio/percentage), constructing and interpreting to-scale Sankey diagrams, and work done = force × distance (joules). All three rest on conservation of energy and dissipation: no real device is 100% efficient, and 'wasted' energy is dissipated (usually to the thermal store of the surroundings), not destroyed. The core activity is a build-and-calculate bench where learners set an input, drag the useful/wasted split, see arrows redraw to scale and an efficiency readout update, plus a work-done tool linking force and distance to W = Fd. Reading-a-Sankey reference, calculation practice, and predict-then-check problems support this.

• 'Wasted energy is lost/destroyed' — it is dissipated (spread out, usually to the thermal store of the surroundings), still conserved; the Sankey's wasted arrow accounts for it.
• Drawing Sankey arrows not to scale, or with output widths that don't sum to the input — breaking conservation in the representation.
• Believing a device can be >100% efficient, or that a more efficient device 'creates' or 'saves' energy rather than wasting less of it.
• Thinking 'useful' vs 'wasted' is a fixed property of an energy type rather than depending on the device's purpose.
• Work-done errors: counting work when there is no movement (holding still), using the wrong (perpendicular) distance, or conflating work, force and power.

• A to-scale Sankey diagram (input arrow splitting into a useful branch and a wasted/dissipated branch; widths summing to the input).
• The efficiency bar/ratio: useful output as a fraction of total input, shown as a percentage.
• The conservation ledger: input = useful + wasted, with the wasted share labelled 'dissipated to surroundings (thermal)'.
• A work-done diagram: a force arrow moving an object through a distance, W = F × d with units (N × m = J).

• Anchor efficiency in conservation FIRST: total input = useful output + wasted (dissipated) energy, so efficiency is the fraction that ends up useful; this makes >100% impossible and explains why the 'wasted' arrow must exist.
• Build Sankey diagrams from the conservation constraint: the input arrow's width must equal the sum of the output arrows' widths — draw to scale (e.g. 1 cm = 10 J) so the proportionality is real, not decorative, and the widths visibly balance.
• Teach 'useful vs wasted' as CONTEXT-dependent, not intrinsic: a lamp's thermal output is wasted, a heater's thermal output is useful — the same transfer is useful or wasted depending on the device's purpose.
• Define work done operationally and confront the everyday meaning: W = Fd is energy transferred when a force moves through a distance IN ITS DIRECTION; holding a heavy bag still (no movement) does NO work in physics, even though it feels effortful.
• Separate the trio of confusable quantities — work/energy (J), force (N), and (next topic) power (W) — with units and worked examples, since students blur them.